The data available on the distances (both from Gaia DR2 and those determined from interstellar Ca II lines) to the brightest stars in the Pleiades ('Seven Sisters' and their 'parents') suggest that these stars highly likely do not form a compact cluster but are localized in front of the main (Pleiades) cluster - at a distance close to that given by Hipparcos. Spectrophotometric distances agree with those from Gaia and Ca II for the brighter stars, but exhibit a large scatter for the stars at the cluster core. According to our study, this effect can be explained by additional ('grey') interstellar extinction due to the presence of larger dust grains within the Pleiades cluster core. Also, we confirm the suggestion that the spatial association of the Pleiades stars and interstellar gas is a result of a chance encounter between the cluster and one or more (at least two) approaching clouds. Indeed, we found that the relatively strong CH+ lines observed in the spectra of the Pleiades stars can be divided into two sets: one with very strong lines of the radical and another with relatively faint ones. Both groups also differ in radial velocities.